public void CreateEquationMatrix_WithUnitCubeInput_CreatesTheCorrectRHS()
{
// Arrange
UnitStrengthRectangularSourcePanel[] sourcePanels = new UnitStrengthRectangularSourcePanel[6]
{
new UnitStrengthRectangularSourcePanel
{
AOver2 = 0.5F, BOver2 = 0.5F, Position = new Vector3(0.5F, 0, 0), U = Vector3.UnitY, V = Vector3.UnitZ
},
new UnitStrengthRectangularSourcePanel
{
AOver2 = 0.5F, BOver2 = 0.5F, Position = new Vector3(-0.5F, 0, 0), U = Vector3.UnitY, V = Vector3.UnitZ
},
new UnitStrengthRectangularSourcePanel
{
AOver2 = 0.5F, BOver2 = 0.5F, Position = new Vector3(0, 0.5F, 0), U = Vector3.UnitZ, V = Vector3.UnitX
},
new UnitStrengthRectangularSourcePanel
{
AOver2 = 0.5F, BOver2 = 0.5F, Position = new Vector3(0, -0.5F, 0), U = Vector3.UnitZ, V = Vector3.UnitX
},
new UnitStrengthRectangularSourcePanel
{
AOver2 = 0.5F, BOver2 = 0.5F, Position = new Vector3(0, 0, 0.5F), U = Vector3.UnitX, V = Vector3.UnitY
},
new UnitStrengthRectangularSourcePanel
{
AOver2 = 0.5F, BOver2 = 0.5F, Position = new Vector3(0, 0, -0.5F), U = Vector3.UnitX, V = Vector3.UnitY
}
};
Vector3 vPanels = new Vector3(10, 0, 0);
double[] correctRHS = new double[6]
{
10,
10,
0,
0,
0,
0
};
// Act
double[,] result = Solver.CreateEquationMatrix(sourcePanels, vPanels);
bool rhsIsCorrect = true;
for (int i = 0; i < correctRHS.Length; i++)
{
if (result[i, 6] != correctRHS[i])
{
rhsIsCorrect = false;
}
}
// Assert
Assert.IsTrue(rhsIsCorrect);
}
public void GlobalSetup()
{
Random random = new Random();
float yaw = (float)random.NextDouble() * 2 * MathF.PI;
float pitch = (float)random.NextDouble() * 2 * MathF.PI;
float roll = (float)random.NextDouble() * 2 * MathF.PI;
Matrix4x4 rotationMatrix =
Matrix4x4.CreateFromYawPitchRoll(yaw, pitch, roll);
_r = new Vector3(
(float)(random.NextDouble() - 0.5) * float.MaxValue,
(float)(random.NextDouble() - 0.5) * float.MaxValue,
(float)(random.NextDouble() - 0.5) * float.MaxValue);
_sourcePanel = new UnitStrengthRectangularSourcePanel
{
AOver2 = (float)random.NextDouble() * float.MaxValue,
BOver2 = (float)random.NextDouble() * float.MaxValue,
Position = new Vector3(
(float)(random.NextDouble() - 0.5) * float.MaxValue,
(float)(random.NextDouble() - 0.5) * float.MaxValue,
(float)(random.NextDouble() - 0.5) * float.MaxValue),
U = Vector3.Transform(Vector3.UnitX, rotationMatrix),
V = Vector3.Transform(Vector3.UnitY, rotationMatrix)
};
}
public void SolveForSourcePanelStrengths_WithUnitCubeInput_SatisfiesTheTangentialFlowConstraint()
{
// Arrange
UnitStrengthRectangularSourcePanel[] sourcePanels = new UnitStrengthRectangularSourcePanel[6]
{
new UnitStrengthRectangularSourcePanel
{
AOver2 = 0.5F, BOver2 = 0.5F, Position = new Vector3(0.5F, 0, 0), U = Vector3.UnitY, V = Vector3.UnitZ
},
new UnitStrengthRectangularSourcePanel
{
AOver2 = 0.5F, BOver2 = 0.5F, Position = new Vector3(-0.5F, 0, 0), U = Vector3.UnitY, V = Vector3.UnitZ
},
new UnitStrengthRectangularSourcePanel
{
AOver2 = 0.5F, BOver2 = 0.5F, Position = new Vector3(0, 0.5F, 0), U = Vector3.UnitZ, V = Vector3.UnitX
},
new UnitStrengthRectangularSourcePanel
{
AOver2 = 0.5F, BOver2 = 0.5F, Position = new Vector3(0, -0.5F, 0), U = Vector3.UnitZ, V = Vector3.UnitX
},
new UnitStrengthRectangularSourcePanel
{
AOver2 = 0.5F, BOver2 = 0.5F, Position = new Vector3(0, 0, 0.5F), U = Vector3.UnitX, V = Vector3.UnitY
},
new UnitStrengthRectangularSourcePanel
{
AOver2 = 0.5F, BOver2 = 0.5F, Position = new Vector3(0, 0, -0.5F), U = Vector3.UnitX, V = Vector3.UnitY
}
};
Vector3 vPanels = new Vector3(10, 0, 0);
// Act
double[] strengths = Solver.SolveForSourcePanelStrengths(sourcePanels, vPanels);
bool flowIsTangentialAtEachControlPoint = true;
for (int i = 0; i < sourcePanels.Length; i++)
{
Vector3 surfaceNormal = Vector3.Cross(sourcePanels[i].U, sourcePanels[i].V);
Vector3 velocity = vPanels;
for (int j = 0; j < sourcePanels.Length; j++)
{
velocity += (float)strengths[j] * Velocity.ComputeSteadyState(sourcePanels[i].Position, sourcePanels[j]);
}
if (Vector3.Dot(velocity, surfaceNormal) != 0)
{
flowIsTangentialAtEachControlPoint = false;
}
}
// Assert
Assert.IsTrue(flowIsTangentialAtEachControlPoint);
}
/// <summary>
/// Computes the steady state velocity potential at the point r due to
/// the unit-strength rectangular source panel provided.
/// </summary>
/// <param name="r">
/// The position vector of the point at which the velocity potential is
/// computed.
/// </param>
/// <param name="sourcePanel">
/// The rectangular source panel causing the velocity potential.
/// </param>
/// <returns>The scalar velocity potential at the point r.</returns>
public static float ComputeSteadyState(
Vector3 r, UnitStrengthRectangularSourcePanel sourcePanel)
{
float velocityPotential = ComputeSteadyState(
sourcePanel.AOver2,
sourcePanel.BOver2,
r - sourcePanel.Position,
sourcePanel.U,
sourcePanel.V);
return(velocityPotential);
}
/// <summary>
/// Computes the steady state velocity at the point r due to the
/// unit-strength rectangular source panel provided.
/// </summary>
/// <param name="r">
/// The position vector of the point at which the velocity is computed.
/// </param>
/// <param name="sourcePanel">
/// The rectangular source panel causing the velocity.
/// </param>
/// <returns>The flow velocity vector at the point r.</returns>
public static Vector3 ComputeSteadyState(
Vector3 r,
UnitStrengthRectangularSourcePanel sourcePanel)
{
Vector3 velocity = ComputeSteadyState(
sourcePanel.AOver2,
sourcePanel.BOver2,
r - sourcePanel.Position,
sourcePanel.U,
sourcePanel.V);
return(velocity);
}
public void CreateEquationMatrix_WithUnitCubeInput_CreatesAMAtrixWith6RowsAnd7Columns()
{
// Arrange
UnitStrengthRectangularSourcePanel[] sourcePanels = new UnitStrengthRectangularSourcePanel[6]
{
new UnitStrengthRectangularSourcePanel
{
AOver2 = 0.5F, BOver2 = 0.5F, Position = new Vector3(0.5F, 0, 0), U = Vector3.UnitY, V = Vector3.UnitZ
},
new UnitStrengthRectangularSourcePanel
{
AOver2 = 0.5F, BOver2 = 0.5F, Position = new Vector3(-0.5F, 0, 0), U = Vector3.UnitY, V = Vector3.UnitZ
},
new UnitStrengthRectangularSourcePanel
{
AOver2 = 0.5F, BOver2 = 0.5F, Position = new Vector3(0, 0.5F, 0), U = Vector3.UnitZ, V = Vector3.UnitX
},
new UnitStrengthRectangularSourcePanel
{
AOver2 = 0.5F, BOver2 = 0.5F, Position = new Vector3(0, -0.5F, 0), U = Vector3.UnitZ, V = Vector3.UnitX
},
new UnitStrengthRectangularSourcePanel
{
AOver2 = 0.5F, BOver2 = 0.5F, Position = new Vector3(0, 0, 0.5F), U = Vector3.UnitX, V = Vector3.UnitY
},
new UnitStrengthRectangularSourcePanel
{
AOver2 = 0.5F, BOver2 = 0.5F, Position = new Vector3(0, 0, -0.5F), U = Vector3.UnitX, V = Vector3.UnitY
}
};
Vector3 vPanels = new Vector3(10, 0, 0);
// Act
double[,] result = Solver.CreateEquationMatrix(sourcePanels, vPanels);
int rows = result.GetLength(0);
int columns = result.GetLength(1);
// Assert
Assert.IsTrue((rows == 6) && (columns == 7));
}
public void CreateEquationMatrix_WithUnitCubeInput_CreatesTheCorrectLHS()
{
// Arrange
UnitStrengthRectangularSourcePanel[] sourcePanels = new UnitStrengthRectangularSourcePanel[6]
{
new UnitStrengthRectangularSourcePanel
{
AOver2 = 0.5F, BOver2 = 0.5F, Position = new Vector3(0.5F, 0, 0), U = Vector3.UnitY, V = Vector3.UnitZ
},
new UnitStrengthRectangularSourcePanel
{
AOver2 = 0.5F, BOver2 = 0.5F, Position = new Vector3(-0.5F, 0, 0), U = Vector3.UnitY, V = Vector3.UnitZ
},
new UnitStrengthRectangularSourcePanel
{
AOver2 = 0.5F, BOver2 = 0.5F, Position = new Vector3(0, 0.5F, 0), U = Vector3.UnitZ, V = Vector3.UnitX
},
new UnitStrengthRectangularSourcePanel
{
AOver2 = 0.5F, BOver2 = 0.5F, Position = new Vector3(0, -0.5F, 0), U = Vector3.UnitZ, V = Vector3.UnitX
},
new UnitStrengthRectangularSourcePanel
{
AOver2 = 0.5F, BOver2 = 0.5F, Position = new Vector3(0, 0, 0.5F), U = Vector3.UnitX, V = Vector3.UnitY
},
new UnitStrengthRectangularSourcePanel
{
AOver2 = 0.5F, BOver2 = 0.5F, Position = new Vector3(0, 0, -0.5F), U = Vector3.UnitX, V = Vector3.UnitY
}
};
Vector3 vPanels = new Vector3(10, 0, 0);
double[,] correctLHS = new double[6, 6]
{
{
Velocity.ComputeSteadyState(sourcePanels[0].Position, sourcePanels[0]).X,
Velocity.ComputeSteadyState(sourcePanels[0].Position, sourcePanels[1]).X,
Velocity.ComputeSteadyState(sourcePanels[0].Position, sourcePanels[2]).X,
Velocity.ComputeSteadyState(sourcePanels[0].Position, sourcePanels[3]).X,
Velocity.ComputeSteadyState(sourcePanels[0].Position, sourcePanels[4]).X,
Velocity.ComputeSteadyState(sourcePanels[0].Position, sourcePanels[5]).X
},
{
Velocity.ComputeSteadyState(sourcePanels[1].Position, sourcePanels[0]).X,
Velocity.ComputeSteadyState(sourcePanels[1].Position, sourcePanels[1]).X,
Velocity.ComputeSteadyState(sourcePanels[1].Position, sourcePanels[2]).X,
Velocity.ComputeSteadyState(sourcePanels[1].Position, sourcePanels[3]).X,
Velocity.ComputeSteadyState(sourcePanels[1].Position, sourcePanels[4]).X,
Velocity.ComputeSteadyState(sourcePanels[1].Position, sourcePanels[5]).X
},
{
Velocity.ComputeSteadyState(sourcePanels[2].Position, sourcePanels[0]).Y,
Velocity.ComputeSteadyState(sourcePanels[2].Position, sourcePanels[1]).Y,
Velocity.ComputeSteadyState(sourcePanels[2].Position, sourcePanels[2]).Y,
Velocity.ComputeSteadyState(sourcePanels[2].Position, sourcePanels[3]).Y,
Velocity.ComputeSteadyState(sourcePanels[2].Position, sourcePanels[4]).Y,
Velocity.ComputeSteadyState(sourcePanels[2].Position, sourcePanels[5]).Y
},
{
Velocity.ComputeSteadyState(sourcePanels[3].Position, sourcePanels[0]).Y,
Velocity.ComputeSteadyState(sourcePanels[3].Position, sourcePanels[1]).Y,
Velocity.ComputeSteadyState(sourcePanels[3].Position, sourcePanels[2]).Y,
Velocity.ComputeSteadyState(sourcePanels[3].Position, sourcePanels[3]).Y,
Velocity.ComputeSteadyState(sourcePanels[3].Position, sourcePanels[4]).Y,
Velocity.ComputeSteadyState(sourcePanels[3].Position, sourcePanels[5]).Y
},
{
Velocity.ComputeSteadyState(sourcePanels[4].Position, sourcePanels[0]).Z,
Velocity.ComputeSteadyState(sourcePanels[4].Position, sourcePanels[1]).Z,
Velocity.ComputeSteadyState(sourcePanels[4].Position, sourcePanels[2]).Z,
Velocity.ComputeSteadyState(sourcePanels[4].Position, sourcePanels[3]).Z,
Velocity.ComputeSteadyState(sourcePanels[4].Position, sourcePanels[4]).Z,
Velocity.ComputeSteadyState(sourcePanels[4].Position, sourcePanels[5]).Z
},
{
Velocity.ComputeSteadyState(sourcePanels[5].Position, sourcePanels[0]).Z,
Velocity.ComputeSteadyState(sourcePanels[5].Position, sourcePanels[1]).Z,
Velocity.ComputeSteadyState(sourcePanels[5].Position, sourcePanels[2]).Z,
Velocity.ComputeSteadyState(sourcePanels[5].Position, sourcePanels[3]).Z,
Velocity.ComputeSteadyState(sourcePanels[5].Position, sourcePanels[4]).Z,
Velocity.ComputeSteadyState(sourcePanels[5].Position, sourcePanels[5]).Z
}
};
// Act
double[,] result = Solver.CreateEquationMatrix(sourcePanels, vPanels);
bool lhsIsCorrect = true;
for (int i = 0; i < 6; i++)
{
for (int j = 0; j < 6; j++)
{
if (result[i, j] != correctLHS[i, j])
{
lhsIsCorrect = false;
}
}
}
// Assert
Assert.IsTrue(lhsIsCorrect);
}
